Multiplying FractionsDate: 07/09/99 at 18:00:43 From: Julie-Anne Subject: How do you multiply fractions? Hi Dr Math. I am being home-schooled and I was wondering if you could help me to understand how to multiply fractions. I just need to know how to multiply fractions like this: 3/5 x 5/8. Thank you, Julie Date: 07/13/99 at 16:59:43 From: Doctor Peterson Subject: Re: How do you multiply fractions? Hi, Julie. There are two important things to know about multiplying fractions: how to do it, which is pretty easy, and how to make it easier, which takes a little more thought. (Yeah, that sounds crazy, but it's generally true that a little more thought at the start makes a lot less work in the end.) The basic idea is simply to multiply the numerators to get the numerator of the product, and multiply the denominators to get the denominator of the product. For your example, 3 5 3 * 5 15 <-- product of numerators --- * --- = ----- = -- 5 8 5 * 8 40 <-- product of denominators Now you have to simplify it; the numerator and denominator are both multiples of 5, so we can divide them by 5 to get 15 15 / 5 3 -- = ------ = --- 40 40 / 5 8 That's the answer, and you could stop here if you like. But, if you look closely, you can see that we just wasted a lot of work: we multiplied 3 and 8 by 5, and then divided the results by 5 again. We can save this work by looking at the product before we actually multiply, and just cancelling out any common factors, namely the 5 we see in both numerator and denominator, knowing we'll just be dividing it out in the end anyway: 1 / 3 5 3 * 5 3 * 1 3 --- * --- = ----- = ----- = --- 5 8 5 * 8 1 * 8 8 / 1 So it's good enough to just learn the rule that says multiply and then simplify; but if you want to save work, you can think a little more before you multiply. You should look through our archives on fractions to see if any other explanations you find will help - sometimes just hearing the same thing explained by people with different ways of expressing themselves can make it click. Here are the archives: http://mathforum.org/dr.math/tocs/fraction.middle.html and here are some specific questions to start with: Fraction Basics http://mathforum.org/dr.math/problems/scamp.7.21.96.html Multiplying Mixed Fractions http://mathforum.org/dr.math/problems/dunphy5.28.98.html Multiplying Fractions by Cancellation http://mathforum.org/dr.math/problems/washington10.9.98.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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